Group #19136934 — subgroups

Subgroups — #19136934

Order 5504.

752 conjugacy classes of subgroups; only the 341 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063282	C₂	1	2	yes	maximal
2	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582750	C₂	1	4	yes	maximal, complemented
4	#14582746	C₂	1	4	yes	maximal
5	#14582745	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄²×Dic₄₃	C₂	1	2	yes	maximal, complemented
7	C₄₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
9	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	#13063282	C₄	1	16	yes	complemented
11	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	8	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
16	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
17	C₄²×D₄₃	C₄	1	8	yes	complemented
18	C₄₃⋊#95	C₂²	1	4	yes	—
19	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
21	#95×C₄₃	C₂²	1	4	yes	—
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂³	1	4	yes	—
27	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₃	C₂³	1	2	yes	—
29	C₂×C₄×D₄₃	—	2	8	no	—
30	C₂×C₄×D₄₃	C₂×C₄	1	8	yes	—
31	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
32	C₂×C₄×D₄₃	C₂×C₄	1	8	yes	—
33	C₄²×C₄₃	C₂×C₄	1	4	yes	—
34	C₄²×C₄₃	C₂×C₄	1	8	yes	complemented
35	(C₂×D₄₃)⋊C₄	C₂×C₄	1	16	yes	—
36	Dic₄₃⋊C₄	C₂×C₄	1	16	yes	complemented
37	C₄×Dic₄₃	—	2	16	no	—
38	C₄×Dic₄₃	C₂×C₄	1	8	yes	—
39	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
40	C₄×Dic₄₃	C₂×C₄	1	8	yes	complemented
41	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
42	C₂²×D₄₃	—	2	4	no	—
43	C₂²×D₄₃	C₂²×C₄	1	4	yes	—
44	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
45	C₂×C₄×C₄₃	—	2	8	no	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
49	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
51	C₂×Dic₄₃	—	2	8	no	—
52	C₂×Dic₄₃	C₂²×C₄	1	8	yes	—
53	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
54	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
55	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
56	C₂×Dic₄₃	#41	1	8	yes	—
57	C₄×D₄₃	—	2	16	no	—
58	C₄×D₄₃	C₄²	1	16	yes	complemented
59	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₄₃	C₂³×C₄	1	2	yes	—
61	C₂²×C₄₃	C₂×#41	1	4	yes	—
62	C₂×D₄₃	—	2	4	no	—
63	C₂×D₄₃	—	2	8	no	—
64	C₂×D₄₃	C₂×C₄²	1	4	yes	—
65	C₄×C₄₃	—	2	4	no	—
66	C₄×C₄₃	—	2	8	no	—
67	C₄×C₄₃	C₂×C₄²	1	4	yes	—
68	Dic₄₃	—	2	8	no	—
69	Dic₄₃	C₂×C₄²	1	4	yes	—
70	Dic₄₃	#117	1	8	yes	complemented
71	C₄×#117	—	43	1	no	maximal, Sylow
72	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
73	C₂×C₄₃	C₂×#117	1	2	yes	—
74	C₂×C₄₃	C₄×#41	1	4	yes	—
75	D₄₃	—	2	4	no	—
76	C₂×#117	—	43	2	no	—
77	C₂²×C₄²	—	43	1	no	—
78	C₄×C₄⋊C₄	—	43	4	no	—
79	C₄×C₂²⋊C₄	—	43	4	no	—
80	#376	—	43	1	no	—
81	#376	D₄₃	1	1	yes	characteristic, complemented
82	C₄³	—	43	2	no	—
83	C₄₃	C₄×#117	1	1	yes	characteristic, complemented, Sylow
84	C₂³×C₄	—	43	1	no	—
85	C₂³×C₄	—	43	2	no	—
86	#117	—	43	16	no	—
87	C₂×C₄⋊C₄	—	43	4	no	—
88	C₂×C₂²⋊C₄	—	43	4	no	—
89	C₂×C₄²	—	43	2	no	—
90	C₂×C₄²	—	43	2	no	—
91	C₂×C₄²	—	43	1	no	—
92	C₂×C₄²	—	43	8	no	—
93	C₂×C₄²	—	43	8	no	—
94	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₄₃	1	2	yes	—
96	#95	—	43	4	no	—
97	#95	C₂×D₄₃	1	4	yes	—
98	C₂⁴	—	43	1	no	—
99	C₂²×C₄	—	43	2	no	—
100	C₂²×C₄	—	43	1	no	—
101	C₂²×C₄	—	43	4	no	—
102	C₂²×C₄	—	43	8	no	—
103	C₂²×C₄	—	43	4	no	—
104	C₂²×C₄	—	43	8	no	—
105	C₂²×C₄	—	86	8	no	—
106	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
107	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
108	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
109	C₄⋊C₄	—	43	16	no	—
110	C₂²⋊C₄	—	43	16	no	—
111	C₄²	—	43	8	no	—
112	C₄²	—	43	4	no	—
113	C₄²	—	43	8	no	—
114	C₄²	—	86	16	no	—
115	C₄²	C₄×D₄₃	1	4	yes	—
116	C₄²	C₄×D₄₃	1	8	yes	complemented
117	C₂³	—	43	4	no	—
118	C₂³	—	43	2	no	—
119	C₂³	—	86	4	no	—
120	C₂³	C₂³×D₄₃	1	1	yes	characteristic
121	C₂×C₄	—	2	8	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	43	2	no	—
124	C₂×C₄	—	43	4	no	—
125	C₂×C₄	—	43	4	no	—
126	C₂×C₄	—	43	8	no	—
127	C₂×C₄	—	43	16	no	—
128	C₂×C₄	—	43	8	no	—
129	C₂×C₄	—	86	16	no	—
130	C₂×C₄	—	86	8	no	—
131	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
132	C₂×C₄	C₂×C₄×D₄₃	1	8	yes	—
133	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
134	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
135	C₂²	—	43	4	no	—
136	C₂²	—	86	4	no	—
137	C₂²	—	86	8	no	—
138	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
139	C₂²	C₂²×C₄×D₄₃	1	2	yes	—
140	C₂²	#41×D₄₃	1	4	yes	—
141	C₄	—	2	4	no	—
142	C₄	—	2	8	no	—
143	C₄	—	43	4	no	—
144	C₄	—	43	8	no	—
145	C₄	—	86	8	no	—
146	C₄	C₄²×D₄₃	1	4	yes	—
147	C₂	—	86	4	no	—
148	C₂	C₂×C₄²×D₄₃	1	1	yes	characteristic
149	C₂	#117×D₄₃	1	2	yes	—
150	C₂	#14583367	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063282

C₂

yes

maximal

C₂×C₄²×D₄₃

C₂

yes

maximal, characteristic

#14582750

C₂

yes

maximal, complemented

#14582746

C₂

yes

maximal

#14582745

C₂

yes

maximal, characteristic, complemented

C₄²×Dic₄₃

C₂

yes

maximal, complemented

C₄₃×#376

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

—

C₂²×C₄×D₄₃

C₂²

yes

characteristic

#13063282

C₄

yes

complemented

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄²×D₄₃

C₄

yes

complemented

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

complemented

(C₂×D₄₃)⋊C₄

C₂×C₄

yes

—

Dic₄₃⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

complemented

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

C₂²×C₄

yes

—

C₂²×D₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

#41

yes

—

C₄×D₄₃

—

C₄×D₄₃

C₄²

yes

complemented

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂³×C₄

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₂×C₄²

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

—

Dic₄₃

—

Dic₄₃

C₂×C₄²

yes

—

Dic₄₃

yes

—

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

C₂×#117

yes

—

C₂×C₄₃

C₄×#41

yes

—

D₄₃

—

C₂×#117

—

C₂²×C₄²

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

#376

D₄₃

yes

characteristic, complemented

C₄³

—

C₄₃

C₄×#117

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

—

#95

—

#95

C₂×D₄₃

yes

—

C₂⁴

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂²×D₄₃

yes

—

107

C₂²×C₄

C₂²×D₄₃

yes

—

108

C₂²×C₄

C₂²×D₄₃

yes

characteristic

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₄²

C₄×D₄₃

yes

—

116

C₄²

C₄×D₄₃

yes

complemented

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂³×D₄₃

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₂×C₄×D₄₃

yes

—

132

C₂×C₄

C₂×C₄×D₄₃

yes

—

133

C₂×C₄

C₂×C₄×D₄₃

yes

—

134

C₂×C₄

C₂×C₄×D₄₃

yes

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂²×C₄×D₄₃

yes

characteristic

139

C₂²

C₂²×C₄×D₄₃

yes

—

140

C₂²

#41×D₄₃

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

C₄²×D₄₃

yes

—

147

C₂

—

148

C₂

C₂×C₄²×D₄₃

yes

characteristic

149

C₂

#117×D₄₃

yes

—

150

C₂

#14583367

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄₃×#376	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	#376	D₄₃
hypocenter	C₄₃	C₄×#117
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₃

commutator

C₂×C₄₃

C₂²×C₄²

Frattini

C₂³

C₂³×D₄₃

Fitting

C₄₃×#376

C₂

socle

C₂³×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
3. #14582750	C₂	semidirect
5. #14582745	C₂	semidirect
6. C₄²×Dic₄₃	C₂	semidirect
7. C₄₃×#376	C₂	semidirect
10. #13063282	C₄	semidirect
17. C₄²×D₄₃	C₄	semidirect
34. C₄²×C₄₃	C₂×C₄	semidirect
36. Dic₄₃⋊C₄	C₂×C₄	semidirect
40. C₄×Dic₄₃	C₂×C₄	semidirect
58. C₄×D₄₃	C₄²	semidirect
70. Dic₄₃	#117	semidirect
81. #376	D₄₃	semidirect
83. C₄₃	C₄×#117	semidirect
116. C₄²	C₄×D₄₃	semidirect

H ≅ G/N

type

3. #14582750

C₂

semidirect

5. #14582745

C₂

semidirect

6. C₄²×Dic₄₃

C₂

semidirect

7. C₄₃×#376

C₂

semidirect

10. #13063282

C₄

semidirect

17. C₄²×D₄₃

C₄

semidirect

34. C₄²×C₄₃

C₂×C₄

semidirect

36. Dic₄₃⋊C₄

C₂×C₄

semidirect

40. C₄×Dic₄₃

C₂×C₄

semidirect

58. C₄×D₄₃

C₄²

semidirect

70. Dic₄₃

#117

semidirect

81. #376

D₄₃

semidirect

83. C₄₃

C₄×#117

semidirect

116. C₄²

C₄×D₄₃

semidirect

Subgroups — #19136934

Conjugacy classes of subgroups

Complements